32 citations · 194 across the 75 of their papers we have counts for
76 papers
Explicit analytic functions defining the images of wave-front singularities
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analy…
Deformations of swallowtails in a 3-dimensional space form
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
This is a continuation of the authors' earlier work on deformations of cuspidal edges. We give a representation formula for swallowtails in the Euclidean 3-space. Using this, we in…
Umbilics of surfaces in the Lorentz-Minkowski 3-space
Naoya Ando, Masaaki Umehara
In this paper, we prove several fundamental properties on umbilics of a space-like or time-like surface in the Lorentz-Minkowski space . In particular, we show that the local…
Null hypersurfaces as wave fronts in Lorentz-Minkowski space
Shintaro Akamine, Atsufumi Honda, Masaaki Umehara +1
In this paper, we show that ``-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the -dimensional Lorent…
Symmetries of cross caps
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singu…
A generalization of Zakalyukin's lemma, and symmetries of surface singularities
Atsufumi Honda, Kosuke Naokawa, Kentaro Saji +2
Zakalyukin's lemma asserts that the coincidence of the images of two wave front germs implies the right equivalence of corresponding map germs under a certain genericity assumption…